Distinct Activities: Shackled by a Common Name?

[Andrew Troup]

Originally Posted by Seaworthy Lass

...I will have a go at illustrating an example, as I think it is a very important concept.....

This is the charplotter track for each of you:

Bravo, Lass

I'm not sure if I can spell irrefutable, but I know it when I see it !

The little pictures showing CF's boat pointing elsewhere than the destination for the entire duration of the trip might seem a small touch, but I'm hoping it will be the telling detail.

People get used to doing this in the situation where the current is always from one direction, but your depiction makes it clear why this is not a winner for reversing current.

I personally think there are now so many different, coherent and persuasive explanations that it would make more sense for anyone who is still not persuaded to mull over what's already on record, than for us to continue generating new ones.

I think this is true even for the more tricky situation, where rather than simply reversing, the current flows from several non-orthogonal directions.

The point to take from all this is:
This particular scenario is not able to be optimised using just a GPS (or any other position fixing method)
You need to know, in advance, what the current rates and directions will be, in order to be able to work out what heading to put the boat on. You also need to know how long it will take to get there, so the problem means going round the mulberry bush several times

I guess a mathematician or software designer would call it a recursive problem. Until you've worked out what course to steer, you don't know when you'll get there, but unless you know when you'll get there, you don't know what course to steer.

If I found myself either needing to (unlikely) or curious to (eminently possible) optimise such a trip, I'd set up a spreadsheet, and use the 'ant on a checkered tablecloth' concept, substituing "Northing" and "Easting" in nautical miles instead of checkers up and checker right, to come up with a computed heading based on a guess at arrival time. The computed heading would derive simply from the ratio of Northing to Easting needed through the water.

The spreadsheet would also compute the (constant) speed needed to cover that distance through the water in the time available.

I would then adjust the arrival time, based on how fast I expected to be able to go in relation to the figure computed, and re-run the simulation.

If conditions changed early in the transit, I'd swap to one of the other (discarded) plans; if they changed later, I'd run a new simulation.

Given I hate motoring, I'm not likely to profit much from such a procedure. Different headings would probably imply different speeds through the water, and apparent windspeed would be another consideration. If part of the plan involves tacking, it could get very complicated indeed.

However, thinking through how I'd do it helps cement the learnings from discussing this with so many deeply knowledgeably and wonderfully communicative people. Thanks to all.

I've done similar spreadsheets in the past, but only to find the optimum time to arrive at the start point for a tricky passage, say round North Cape, through Cook or Foveaux Strait or Current Basin, all in NZ in order not just to trim as much as twelve hours from a passage, but more importantly to avoid wind against tide in places where, to quote the NZ Pilot, "Prayer may be of assistance" when both are strong.

I've never used a spreadsheet to calculate a heading to steer, but I think it would be much preferable to doing it on paper, given a complex sequence of strong current vectors in relation to available boatspeed, and the recursive (if that's the word) nature of the calculation.

[goboatingnow]

Originally Posted by Seaworthy Lass

CF's speed relative to the water is 5 knots (fixed throughout the journey as he is keeping constant revs). The current is pushing the boat at 2 knots perpendicular to the line between A and B. So we can use Pythagoras' triangle to work out CF's VMG (see diagram below).

The VMG squared plus two squared = five squared.
So VMG squared = 25 - 4 = 21
So VMG = 4.58

The formula for the angle of deviation (and therefore the compass heading in this case as the destination point is magnetically north of the departure point) is as follows:
Sinθ = 2/5
where θ is the angle
This works out to be 24 degrees.

I see sorry I brain a bit slow tonight I should have seen that. I was wondering If you were actually trying to model the autopilot performance. ( which is worse then your calculations )



Dave

[goboatingnow]

Andrew , it can only be done two ways. Either you have advance tidal information , hence you just draw the vectors on your chart and add them up and derive a single course wide CTS. Alternatively you can run hourly or multi hourly CTS based on assumptions of what you see the boat being subjected too.

Often one has some information but not enough conclusive information. Equally,in long journeys it is useful to break them up into several legs and re compute CTS

I don't think anyone disputes the symmetrical tidal model and CTS. What would be interesting is to compute an error graph for various non symmetrical but partly reversing currents or currents that don't flow perpendicular to the direction of travel. Hence it would allow one to see how much or how little advantage the single CTS method gives.

Dave

[Seaworthy Lass]

Originally Posted by Andrew Troup

......The little pictures showing CF's boat pointing elsewhere than the destination for the entire duration of the trip might seem a small touch, but I'm hoping it will be the telling detail.

People get used to doing this in the situation where the current is always from one direction, but your depiction makes it clear why this is not a winner for reversing current.

I struggled to find an explanation that might get through to the disbelievers. So many posts had already given great examples but not got the message through.

I thought a diagram of what the charplotter would show for the track and positions of the boats (and the angle of the boats as well) may make it easier to view and understand .

Originally Posted by Andrew Troup

I personally think there are now so many different, coherent and persuasive explanations that it would make more sense for anyone who is still not persuaded to mull over what's already on record, than for us to continue generating new ones.

I'm done. It was a final attempt

Originally Posted by Andrew Troup

The point to take from all this is:
This particular scenario is not able to be optimised using just a GPS (or any other position fixing method)
You need to know, in advance, what the current rates and directions will be, in order to be able to work out what heading to put the boat on. You also need to know how long it will take to get there, so the problem means going round the mulberry bush several times
.......

Yes, neither a GPS or chartplotter will give you the compass heading you need to follow to make your journey in the shortest possible time. Accurate calculations are hard as the exact current is usually unknown and the boat speed is only a guess as well, but at least it can be factored in.

Been an interesting discussion. Thanks all.

[carstenb]

Originally Posted by Seaworthy Lass

I humbly suggest you check your calculations. The sum of five squared and two squared is 29 not 27 (easy error to make if you are in a hurry).

.

That is what happens when you have ten thumbs and are using your Iphone as a calculator.

[Dockhead]

Originally Posted by goboatingnow

Andrew , it can only be done two ways. Either you have advance tidal information , hence you just draw the vectors on your chart and add them up and derive a single course wide CTS. Alternatively you can run hourly or multi hourly CTS based on assumptions of what you see the boat being subjected too.

Often one has some information but not enough conclusive information. Equally,in long journeys it is useful to break them up into several legs and re compute CTS

I don't think anyone disputes the symmetrical tidal model and CTS. What would be interesting is to compute an error graph for various non symmetrical but partly reversing currents or currents that don't flow perpendicular to the direction of travel. Hence it would allow one to see how much or how little advantage the single CTS method gives.

Dave

It's all the same whether the tide is symmetrical or not. Seaworth Lass' excellent drawing shows what happens when you sail the hypotenuse of the triangle -- it's the longer leg. Anytime the water is moving, you have a choice of sailing a straight line through the water, or not. If you deviate from the straight line through the water -- the constant heading -- whether through ignorance or through not having enough data to compute a good CTS, then you are adding miles. Only if the water is moving at exactly the same speed and direction over the whole passage, will the straight line through the water coincide with a straight line over ground.

Andrew Troup had a subtle insight about the recursiveness of the calculation of CTS. It is very true, and it means that even with perfect information about tidal streams, the calculation can be very complex and indeed impossible to do by hand. So far we have assumed that we could know our arrival time with reasonable certainty. Of course we don't know very well -- in a sailboat, your speed is always changing.

But more importantly -- and this is really important -- we don't know the distance. If we are sailing to Cherbourg from Needles with a symmetrical tide, so that CTS approximately equals bearing to waypoint, then we know it's close to 60 miles. But if there is a big difference between CTS and BTW then your passage through water will be more than 60 miles. More or less time in passage means more or less time exposed to different currents, so will change the correct CTS. So yes -- it's recursive -- you have to guess, then run the numbers, then refine the number (time on passage, once you understand the distance better), then run the numbers again.

With very complicated rotary currents like around the Channel Islands, it becomes too complicated for my feeble brain. Need a good computer program to do it. For crossing the Gulf Stream or crossing the English Channel, it is surprising what amazingly good results you get from rather approximate information and fairly vague guesses. I am rarely more than a mile off. There are some complicated mathematical principles at work, I suspect, involving perhaps fuzzy numbers and approximations (otherwise known as "magic" to those of us who are uninitiated). I'll try to remember to ask my brother about it (a math & physics prof).

To step three steps back -- the purpose of this part of the discipline of navigation is, to put it very crudely but perhaps, aptly, is to avoid arriving downtide of your destination. That is really the main point, isn't it? To work with the currents instead of fighting them, to steer in a way that lets them sweep you to your destination, instead of crabbing along the rhumb line, always sailing the hypotenuse of Seaworthy Lass' excellent triangle. Arriving uptide even by several miles is not a big problem (so you want to err on that side when you are making your guesses and approximations). Even if you only realize it an hour out from your destination, you just bear off a little and let the tide bring you in. Even a single mile downtide, on the other hand, can be a total b*tch, especially off the coast of Normandy where the currents are faster than on the English coast. They really rip when you get close to C-bourg, and in a small boat in light winds and at springs you might not even be able to get there at all, if an hour out you are even a little too far downtide (that is, if you are not far enough uptide of the rhumb line -- if you don't have enough XTE). In which case you divert to Alderny

By the way, that's another good demonstration of CTS versus GPS track sailing across currents. If the current is faster than your boat speed, there comes a point where you will never even arrive by GPS track navigation, when you can make it comfortably by steering constant CTS. The difference between the approaches is exaggerated, the higher the current speed is compared to your boat speed. We get 6 knots at springs in much of the English Channel; up to 12 around Alderny, so this is not at all a hypothetical question at all, if we are talking about a small boat making 5 knots.

[Seaworthy Lass]

Originally Posted by Dockhead

........
To step three steps back -- the purpose of this part of the discipline of navigation is, to put it very crudely but perhaps, aptly, is to avoid arriving downtide of your destination. That is really the main point, isn't it? To work with the currents instead of fighting them, to steer in a way that lets them sweep you to your destination, instead of crabbing along the rhumb line, always sailing the hypotenuse of Seaworthy Lass' excellent triangle. Arriving uptide even by several miles is not a big problem (so you want to err on that side when you are making your guesses and approximations). Even if you only realize it an hour out from your destination, you just bear off a little and let the tide bring you in. Even a single mile downtide, on the other hand, can be a total b*tch, especially off the coast of Normandy where the currents are faster than on the English coast. They really rip when you get close to C-bourg, and in a small boat in light winds and at springs you might not even be able to get there at all, if an hour out you are even a little too far downtide (that is, if you are not far enough uptide of the rhumb line -- if you don't have enough XTE). In which case you divert to Alderny

By the way, that's another good demonstration of CTS versus GPS track sailing across currents. If the current is faster than your boat speed, there comes a point where you will never even arrive by GPS track navigation, when you can make it comfortably by steering constant CTS. The difference between the approaches is exaggerated, the higher the current speed is compared to your boat speed. We get 6 knots at springs in much of the English Channel; up to 12 around Alderny, so this is not at all a hypothetical question at all, if we are talking about a small boat making 5 knots.

Some excellent points have been raised in this post underlining the importance of making at least rough calculations about compass heading required for a leg of a passage.

For the example I gave in post # 340, many people would shrug their shoulders and say "what does it matter if I arrive 22 minutes after Dockhead, I am cruising, not racing".

But if the current had changed direction a bit earlier and started increasing significantly, CaptForce may not have reached his destination for hours after Dockhead had arrived.

Making these calculations at least roughly is not difficult if the current is approximately perpendicular to the line between departure and arrival points - I just assume constant speed and look at the expected current at each hour and then cancel out opposing current and see what I am left with for how long. It's then just one lot of figures I need to work on.

As you said, importantly this also allows you to plan the passage to avoid adverse current (or take advantage of it when it is favourable) .

[Dockhead]

Originally Posted by Seaworthy Lass

For the example I gave in post # 340, many people would shrug their shoulders and say "what does it matter if I arrive 22 minutes after Dockhead, I am cruising, not racing".

A valid point, and no doubt many people will just say -- "Screw it, let the plotter calculate my route, and let the pilot steer it, while I lounge in the cockpit."

We do it for fun, so if that makes you happier, then go for it.

But for many other people, getting sail trim just right, for example, is not primarily in order to arrive 22 minutes earlier, but for the satisfaction of doing it well.

Same thing applies to navigation. "Screw it, I'll just crab across along the rhumb line, it's only an hour extra" is one way to get there, and maybe it doesn't matter to some people. But if you sail for fun, including the fun of learning complex disciplines and doing it well, surely there is no satisfaction in that approach. Surely it's a lot more fun to do it right and get there with the help of the current, instead of fighting it the whole way.


And of course some times even cruisers really do need to get somewhere sooner rather than later. That's certainly often the case when I'm cruising, especially with my father on board. We don't drink underway, but 17:00 cocktail hour is a sacred event. So my father gets really cross if the anchor is not down by 16:45. He doesn't care about much else about my passage plans, but he stringently checks the ETA, to make sure there is no conflict with cocktail hour. So it behooves me not to screw up the navigation!

[carstenb]

Dockhead,

Your father is obviously a man of impeccable taste. I agree with completely. My happy hour is also pretty sacred.

I mean, a man could die of thirst out there...............

jes sayin'

[Seaworthy Lass]

Originally Posted by Dockhead

A valid point, and no doubt many people will just say -- "Screw it, let the plotter calculate my route, and let the pilot steer it, while I lounge in the cockpit."

We do it for fun, so if that makes you happier, then go for it.

But for many other people, getting sail trim just right, for example, is not primarily in order to arrive 22 minutes earlier, but for the satisfaction of doing it well.

Same thing applies to navigation. "Screw it, I'll just crab across along the rhumb line, it's only an hour extra" is one way to get there, and maybe it doesn't matter to some people. But if you sail for fun, including the fun of learning complex disciplines and doing it well, surely there is no satisfaction in that approach. Surely it's a lot more fun to do it right and get there with the help of the current, instead of fighting it the whole way.


And of course some times even cruisers really do need to get somewhere sooner rather than later. That's certainly often the case when I'm cruising, especially with my father on board. We don't drink underway, but 17:00 cocktail hour is a sacred event. So my father gets really cross if the anchor is not down by 16:45. He doesn't care about much else about my passage plans, but he stringently checks the ETA, to make sure there is no conflict with cocktail hour. So it behooves me not to screw up the navigation!

+1! Oh, yes, the pleasure in the challenge of doing something well is truly satisfying .

Your father sounds like he has the right idea too . All work certainly stops on board our boat at 4pm while at anchor. It's a very civilised hour to sit back and enjoy the scenery if we haven't already been doing so!

[goboatingnow]

It's all the same whether the tide is symmetrical or not. Seaworth Lass' excellent drawing shows what happens when you sail the hypotenuse of the triangle -- it's the longer leg. Anytime the water is moving, you have a choice of sailing a straight line through the water, or not. If you deviate from the straight line through the water -- the constant heading -- whether through ignorance or through not having enough data to compute a good CTS, then you are adding miles. Only if the water is moving at exactly the same speed and direction over the whole passage, will the straight line through the water coincide with a straight line over ground.

Jeepers Dockhead, Im not arguing about the Maths, I teach chartwork for heavens sake

What I was commenting about is that the Combined CTS method works when you have good data and consistent performance. It also provides the biggest advantage when there is a 90 tidal stream. for all other tides there is an advantage to the CTS method that decreases towards the "track" method, as the tides streams move parallel to the course,

Symetrical tides are always used to illustrate the advantage of the CTS method, there a reason for that.

Like everything if you know how to apply it, you can use combinations of GPS , CTS and an ounce of noggin, you may not get 100% advantage but Ill argue that at sea there are so many variables at work that often the semi- intituitive approach works just as well.

Only if the water is moving at exactly the same speed and direction over the whole passage, will the straight line through the water coincide with a straight line over ground.

Same direction yes, it doesnt matter if the speed is different, your boat moves through the water at the water related speed, Where there is a significant component of the tide, assigned with the course , then the GPS method is similar to the CTS method.

To step three steps back -- the purpose of this part of the discipline of navigation is, to put it very crudely but perhaps, aptly, is to avoid arriving downtide of your destination. That is really the main point, isn't it? To work with the currents instead of fighting them, to steer in a way that lets them sweep you to your destination, instead of crabbing along the rhumb line, always sailing the hypotenuse of Seaworthy Lass' excellent triangle. Arriving uptide even by several miles is not a big problem (so you want to err on that side when you are making your guesses and approximations). Even if you only realize it an hour out from your destination, you just bear off a little and let the tide bring you in. Even a single mile downtide, on the other hand, can be a total b*tch, especially off the coast of Normandy where the currents are faster than on the English coast. They really rip when you get close to C-bourg, and in a small boat in light winds and at springs you might not even be able to get there at all, if an hour out you are even a little too far downtide (that is, if you are not far enough uptide of the rhumb line -- if you don't have enough XTE). In which case you divert to Alderny

whether you use a finely worked out CTS or you use an intuitive and hence recursive method, all good mariners want to end up-tide.

Im not the one arguing against the method, Im merely pointing out that we rarely work out the CTS "advantage" in anything other then symmetrical tides, at some point it may be useful to abandon complex calculations in advance and suck it and see ( properly) as the actual real advantage may be small or not material to the overall crossing. ( as in where there is a significant tidal component in line with the intended direction )

Dave

[Dockhead]

Originally Posted by goboatingnow

Jeepers Dockhead, Im not arguing about the Maths, I teach chartwork for heavens sake

What I was commenting about is that the Combined CTS method works when you have good data and consistent performance. It also provides the biggest advantage when there is a 90 tidal stream. for all other tides there is an advantage to the CTS method that decreases towards the "track" method, as the tides streams move parallel to the course,

Symetrical tides are always used to illustrate the advantage of the CTS method, there a reason for that.

Like everything if you know how to apply it, you can use combinations of GPS , CTS and an ounce of noggin, you may not get 100% advantage but Ill argue that at sea there are so many variables at work that often the semi- intituitive approach works just as well.

Same direction yes, it doesnt matter if the speed is different, your boat moves through the water at the water related speed, Where there is a significant component of the tide, assigned with the course , then the GPS method is similar to the CTS method.




whether you use a finely worked out CTS or you use an intuitive and hence recursive method, all good mariners want to end up-tide.

Im not the one arguing against the method, Im merely pointing out that we rarely work out the CTS "advantage" in anything other then symmetrical tides, at some point it may be useful to abandon complex calculations in advance and suck it and see ( properly) as the actual real advantage may be small or not material to the overall crossing. ( as in where there is a significant tidal component in line with the intended direction )

Dave

Well, symmetrical tides across the English Channel makes for the simplest calculations and are the ideal teaching case.

I must not be understanding you -- you teach chartwork, after all so clearly must understand all this much better than I do -- but I don't see how you can say that there's less advantage with a unidirectional (non-symmetrical) current with varying speeds.

The classical case is crossing the Gulf Stream. If you follow the GPS track method you are really screwed, because you arrive at the accelerated current on the rhumb line, only to get swept N and end up fighting your way all the way to the Bahamas. This is a really dramatic illustration of the value of the combined CTS method. Only by calculating a CTS from the beginning of the passage will you hit the Gulf Stream at the right spot so that it sets you into the right position to arrive without fighting the current. That right spot to enter the Gulf Stream will be far S of the rhumb line, so there will be a very large difference between the GPS track method and combined CTS method, although the current does not change directions.

If the current is not perpendicular to your path, the set of the current will be less than the current's speed. But for any given amount of set, you still have the same problem. It is the variation of strength of the current over your passage which creates the difference in results between the two methods.

Or probably I didn't understand correctly, what you were saying.

[goboatingnow]

If the current is not perpendicular to your path, the set of the current will be less than the current's speed. But for any given amount of set, you still have the same problem. It is the variation of strength of the current over your passage which creates the difference in results between the two methods

Dockhead, The combined CTS method, only provides the best advantage if there is a cross tide. ( ie max error) if the tide was solely parallel to the course, even though it varied in speed, there would be no difference between the track method and the CTS method, ( Ie zero error) . CTS being purely a Course computation. ( in the way that it is normally used I mean) Hence in complex tides, there is an error using the ground route that varies from zero to maximum in a non linear fashion, In some cases like symmetrical tides, its obvious which to use and most do. In other cases, either becuase we are lacking data, speed or direction turn out to be variable, we have a semi -intitutive method that combines both, hence there is a error. ( by error i mean +- advantage)

Again your Gulf stream takes a perpendicular tide, which is always the most demonstrative on the examples. I dont dispute that at all.

I suppose where I'm coming from , is I often get asked, in class, OK if I just use my GPS on track mode ( which isnt a mode I ever use BTW) then what is the "disadvantage", ie what is the quantifiable time I have lost, In symmetrical tides this is easy enough to demonstrate , however in other tidal streams that error is less, and many people would ( and do ) just accept the loss of time, over the need to do the computation, especially when in real life , most of the time you have to reassess and recompute and other variables introduce further uncertainty.

Its a small side-issue , thats what Im setting up Mathematica for, to try and model the actual advantage for a selection of streams , not just perpendicular.

Im not arguing that if you want to time your arrival at a certain place ( not just figure out the optimim course), then you must allow for tide, using the CTS or GPS method

DAve

[Seaworthy Lass]

Originally Posted by goboatingnow

......I don't think anyone disputes the symmetrical tidal model and CTS. What would be interesting is to compute an error graph for various non symmetrical but partly reversing currents or currents that don't flow perpendicular to the direction of travel. Hence it would allow one to see how much or how little advantage the single CTS method gives.

The current doesn't have to be symmetrical at all to gain the maximum advantage, the components just have to add up to zero for a passage. This is an important distinction.

Originally Posted by goboatingnow

......Same direction yes, it doesnt matter if the speed is different, your boat moves through the water at the water related speed, Where there is a significant component of the tide, assigned with the course , then the GPS method is similar to the CTS method.

It does actually matter if your log speed varies, as it is lengthens or shortens your journey (or your time spent subjected to a certain current) and you no longer have zero total current effect.

I do agree with you though that the advantage of following a constant compass heading is maximum when the current is purely at 90 degrees to the line between departure and arrival points (unless of course if arriving sooner has you completing the passage just before the current alters really unfavourably .

The reason that examples would be given for tides with zero total current is the calculations are very simple compared to mind boggling difficult to do accurately .

[Seaworthy Lass]

Originally Posted by Seaworthy Lass

It does actually matter if your log speed varies, as it is lengthens or shortens your journey (or your time spent subjected to a certain current) and you no longer have zero total current effect.
......

Oops, my mind was still on the other issue when I typed that.
GoBoatings comment referred to changing amount of current, not boat speed.

I meant it does actually matter if the amount of current varies - the tracks of the two boats will not be the same on the chartplotter if current amount varies along the way

Sorry folks, must be getting tired, time to hit the sack! Thanks goodness I am not crossing any currents at the moment or goodness knows where I may have ended up .